Embibe Experts Solutions for Exercise 2: EXERCISE

$x+ky-z=0,3x-ky-z=0$ and $x-3y+z=0$ has non-zero solution for $k=$

If $a_{1}x+b_{1}y+c_{1}z=0, a_{2}x+b_{2}y+c_{2}z=0, a_{3}x+b_{3}y+c_{3}z=0$ and $\left|\begin{array}{ccc}{a}_1& b_1& c_1\\ a_2& b_2& c_2\\ a_3& b_3& c_3\end{array}\right|=0$, then the given system has -

The existence of the unique solution of the system $x+y+z=\lambda , 5x-y+\mu z=10, 2x+3y-z=6$ depends -

The number of solution of the following equations $x_2-x_3=1, -x_1+2x_3=-2, x_1-2x_2=3$ is-

The solution of the equation $\left[\begin{array}{ccc} 1& 0& 1\\ -1& 1& 0\\ 0& -1& 1\end{array}\right]\left[\begin{array}{l}x\\ y\\ z\end{array}\right]=\left[\begin{array}{l}1\\ 1\\ 2\end{array}\right]$ is $(x,y,z)=$

If $x+ay+a^{2}z=0$,  $x+by+b^{2}z=0$, $x+cy+c^{2}z=0$ ,  $a\ne b\ne c$,  then given system of equations -

If $A$ is a square matrix of order $3$, then the true statement is (Where $I$ is unit matrix) -

Let the determinant of a $3\times 3$ matrix $A$ be $2$, then $B$ is a matrix defined by $B=5A^2$. Then det of $B$ is -